Emergence of Volatility

Volatility is not injected into markets from outside; it emerges from the trading itself. Exchanges run a continuous auction, every order carries a private interpretation of the same public information, and news forces those interpretations to be revised all at once — so prices jump, herding amplifies the jumps, and algorithmic trading executes the herding at machine speed. The aggregation of millions of such decisions is why volatility can be measured precisely and predicted only roughly.

One theoretical point is worth keeping, because it explains a failure you will meet in practice. In an ideal model, volatility would follow a stable distribution — the same statistical shape at every time scale, so that weekly behavior could be derived from daily and daily from intraday. Real markets do not oblige: no common model of volatility survives the trip across time scales intact, which is one reason the $\sqrt{T}$ scaling rule below is a convention, not a law.